Setting Up Equations

Date: 11/26/97 at 21:39:22
From: Jessica Shortreed-Hume
Subject: Setting up equations
An airplane travels eight times as fast as a car. The difference in
their speeds is 420 km/h. How fast is each vehicle travelling?
I tried to set up a formula but it won't work no matter what I try.
Help!

Date: 11/30/97 at 21:57:40
From: Doctor Allan
Subject: Re: Setting up equations
Hello Jessica!
What you need to do is put the information you have into mathematical
equations. Let me help you with the setup - then you can try to do the
math yourself.
Let's call the speed of the car x and the speed of the plane y. We are
told that the speed of the plane is eight times the speed of the car.
This means that
(1) 8x = y
Furthermore we are told that the difference in their speeds is
420 km/h. We get
(2) y-x = 420
Do you understand how I did this part? If you did you are quite close
to the answer.
In equation (1) you are told that every time you see a y, you can
replace it with 8x. So this is what you do in equation (2), enabling
you to get a value for y. This value can be substituted into equation
(1) yielding a value for x.
Since x and y were the speeds of the car and the plane, you can put
your answer back into words once you find x and y.
I hope this helps. If it doesn't, please write again.
-Doctor Allan, The Math Forum
Check out our web site! http://mathforum.org/dr.math/